Did I download Blender correctly, or was it CG Cookie?
Try downloading Blender from this page https://www.blender.org/download/.

Make sure you get the correct version for your operating system.

You can also download a program file that does not require installing by downloading the zip.

Simply unzip the folder to your desktop, and run the program (it will be the file "blender" and will be a program file. [or application/executable, depending on your os.])

Or you can download the "bleeding edge" test builds from here. It is the most recent version of Blender, and is a kind of test build, so be ware, it may not be stable.